Let $f$ be a 3D scalar field. Is the expression $\text{curl}(\nabla \times f)$ a scalar field, a vector field, or undefined? Choose 1 answer: Choose 1 answer: (Choice A) A Scalar field (Choice B) B Vector field (Choice C) C Undefined
The 3D curl, which takes a vector field and gives a vector field, can also be written in two ways: $\text{curl}(F) = \nabla \times F$ Therefore, $\text{curl}(\nabla \times f)$ is the curl of the curl of a 3D scalar field. Because the curl only takes vector fields, the curl of a scalar field is undefined. The expression $\text{curl}(\nabla \times f)$ is undefined.